0). Preamble: Loading Packages and Data; Data Preperation

a). Load Packages

library(tidyverse)
library(ggplot2)
library(ggcorrplot)
library(knitr)   # contains kable() function
library(partykit)
## Warning: package 'partykit' was built under R version 4.0.4
## Warning: package 'libcoin' was built under R version 4.0.4
library(caret)
library(rpart)
library(randomForest)
## Warning: package 'randomForest' was built under R version 4.0.4
library(pROC)
library(leaps)
library(glmnet)
library(gbm)
## Warning: package 'gbm' was built under R version 4.0.4
set.seed(95791)

b). Import and Initial Data Prep

Be sure to set working directory to source file location

#bring in housing data
housing <- read.csv(file = "AmesHousing.csv", header = TRUE)

c). Preparing Dataset for Analysis

i). Removing NA values from dataset

# #BSMT Numeric--This may need to be addressed differently. You can have a basement without a bathroom, and zero values already exist.
# Bsmt.Full.Bath
# Bsmt.Half.Bath
#Garage.Yr.Blt data is a Year value may need to be adjusted.
#Mas.Vnr.Area

if (sum(is.na(housing)) >0) {
  
  DNE.Cols = c(74,75,76,32,33,34,35,37,8,59,65,66,62,60,29,30)
  zero.Cols = c(3, 5, 49,50,61,63,64,28)
  zero.Cols.alt = c(36,38,39,40) #These are all from one record (1342). Maybe just omit the record?
  catchall.cols = seq(1, 82, by=1)
  
  for (i in DNE.Cols){
    housing[[i]][is.na(housing[[i]]) | housing[[i]] == ""] = "DNE" # These are stored as "", not NA, so it's not picking them up
  }
  
  for (i in zero.Cols){
    housing[[i]][is.na(housing[[i]])] = 0
  }
  
  for (i in zero.Cols.alt){
    housing[[i]][is.na(housing[[i]])] = 0
  }
   
  # for (i in catchall.cols){
  #   housing[[i]][housing[[i]]==""] <- NA
  # }
  # 
  # for (i in catchall.cols){
  #   housing[[i]][is.na(housing[[i]])] = 0
  # }
  #Verify NAs are removed
  sum(is.na(housing))
}
## [1] 0

ii). Verify absences of NA values

sum(is.na(housing))
## [1] 0
#Show columns that have at least one NA
housing[, colSums(is.na(housing)) > 0]
## data frame with 0 columns and 2930 rows
#Show rows that have at least one NA
housing[rowSums(is.na(housing)) > 0,]
##  [1] ï..Order        PID             MS.SubClass     MS.Zoning      
##  [5] Lot.Frontage    Lot.Area        Street          Alley          
##  [9] Lot.Shape       Land.Contour    Utilities       Lot.Config     
## [13] Land.Slope      Neighborhood    Condition.1     Condition.2    
## [17] Bldg.Type       House.Style     Overall.Qual    Overall.Cond   
## [21] Year.Built      Year.Remod.Add  Roof.Style      Roof.Matl      
## [25] Exterior.1st    Exterior.2nd    Mas.Vnr.Type    Mas.Vnr.Area   
## [29] Exter.Qual      Exter.Cond      Foundation      Bsmt.Qual      
## [33] Bsmt.Cond       Bsmt.Exposure   BsmtFin.Type.1  BsmtFin.SF.1   
## [37] BsmtFin.Type.2  BsmtFin.SF.2    Bsmt.Unf.SF     Total.Bsmt.SF  
## [41] Heating         Heating.QC      Central.Air     Electrical     
## [45] X1st.Flr.SF     X2nd.Flr.SF     Low.Qual.Fin.SF Gr.Liv.Area    
## [49] Bsmt.Full.Bath  Bsmt.Half.Bath  Full.Bath       Half.Bath      
## [53] Bedroom.AbvGr   Kitchen.AbvGr   Kitchen.Qual    TotRms.AbvGrd  
## [57] Functional      Fireplaces      Fireplace.Qu    Garage.Type    
## [61] Garage.Yr.Blt   Garage.Finish   Garage.Cars     Garage.Area    
## [65] Garage.Qual     Garage.Cond     Paved.Drive     Wood.Deck.SF   
## [69] Open.Porch.SF   Enclosed.Porch  X3Ssn.Porch     Screen.Porch   
## [73] Pool.Area       Pool.QC         Fence           Misc.Feature   
## [77] Misc.Val        Mo.Sold         Yr.Sold         Sale.Type      
## [81] Sale.Condition  SalePrice      
## <0 rows> (or 0-length row.names)

iii). Factors reorder

housing.factors <- housing

housing.factors$Exter.Cond <- factor(housing.factors$Exter.Cond, levels = c('DNE', 'Po', 'Fa', 'TA', 'Gd', 'Ex'))
housing.factors$Exter.Qual <- factor(housing.factors$Exter.Qual, levels = c('DNE', 'Po', 'Fa', 'TA', 'Gd', 'Ex')) 
housing.factors$Bsmt.Qual <- factor(housing.factors$Bsmt.Qual, levels = c('DNE', 'Po', 'Fa', 'TA', 'Gd', 'Ex'))
housing.factors$Bsmt.Cond <- factor(housing.factors$Bsmt.Cond, levels = c('DNE', 'Po', 'Fa', 'TA', 'Gd', 'Ex'))
housing.factors$Kitchen.Qual <- factor(housing.factors$Kitchen.Qual, levels = c('DNE', 'Po', 'Fa', 'TA', 'Gd', 'Ex'))
housing.factors$Fireplace.Qu <- factor(housing.factors$Fireplace.Qu, levels = c('DNE', 'Po', 'Fa', 'TA', 'Gd', 'Ex'))
housing.factors$Garage.Cond <- factor(housing.factors$Garage.Cond, levels = c('DNE', 'Po', 'Fa', 'TA', 'Gd', 'Ex'))
housing.factors$Garage.Qual <- factor(housing.factors$Garage.Qual, levels = c('DNE', 'Po', 'Fa', 'TA', 'Gd', 'Ex'))
housing.factors$Pool.QC <- factor(housing.factors$Pool.QC, levels = c('DNE', 'Po', 'Fa', 'TA', 'Gd', 'Ex'))
housing.factors$Heating.QC <- factor(housing.factors$Heating.QC, levels = c('DNE', 'Po', 'Fa', 'TA', 'Gd', 'Ex'))

housing.factors$MS.SubClass <- factor(housing.factors$MS.SubClass , levels = c(20, 30, 40, 45, 50, 60, 70, 75, 80, 85, 90, 120, 150, 160, 180, 190))

# Print any columns with missing values
for(v in names(housing.factors)) {
  n_na = sum(is.na(housing.factors[v]))
  if(n_na > 0) {print(v); print(n_na)}
}

1. Exploratory Data Analysis

b). Correlation Plot

cor.housing.sales <- cor(numeric.df[,-1:-2])
ggcorrplot(cor.housing.sales)

Once the dataset has been scrubbed, initial exploratory data analysis is conducted. The first analysis is looking at all numeric vectors in the dataset and checking to see if there are any correlations between variables.

Correlations:

Total.Bsmt.SF ~ X1st.Flr.SF (0.80)

Gr.Liv.Area ~ TotRms.AbvGrd (0.81)

Garage.Cars ~ Garage.Area (0.89)

c). Box Plots of quals

qual.cols.vec <-  c(29, 30, 32, 33, 42, 55, 59, 65, 66, 74)
for (i in qual.cols.vec){
  boxplots <- qplot(data = housing.factors, x = housing.factors[,i], y = SalePrice, geom = "boxplot", xlab = paste(colnames(housing.factors)[i]))
  print(boxplots)
  
}

qual.cols.vec <-  c(3, 4, 7, 8 , 9 , 10, 11, 12, 13, 14, 15, 16, 17,
                    18, 23, 24, 25, 26, 27, 31, 35, 37, 41, 44, 57,
                    60, 62, 67, 75, 76, 80, 81)
for (i in qual.cols.vec){
  boxplots <- qplot(data = housing.factors, x = housing.factors[,i], y = SalePrice, geom = "boxplot", xlab = paste(colnames(housing.factors)[i]))
  print(boxplots)
  
}

#Note all variables that are used in models, so we can retain their box plots:

2. Sales Price Prediction Model (Khadija w/ assistance)

Tip: think about performance metrics other than MSE: MAE, relative error, etc. > A predictive model that uses housing sale prices 2006-2009.

a). Forward and Backward Stepwise Model

i). Finding the Optimal Stepwise Model

# Forward and backward stepwise (best subset will be too time-intensive)
nvmax = 1000 #ncol(housing)
model = map(
  .x = c('forward', 'backward'),
  .f = ~regsubsets(SalePrice ~ .,
           data = housing.factors[housing.factors$Yr.Sold != 2010, ],
           nvmax = nvmax, method = .x, really.big = F)
)
## Warning in leaps.setup(x, y, wt = wt, nbest = nbest, nvmax = nvmax, force.in =
## force.in, : 15 linear dependencies found
## Reordering variables and trying again:
## Warning in rval$lopt[] <- rval$vorder[rval$lopt]: number of items to replace is
## not a multiple of replacement length

## Warning in rval$lopt[] <- rval$vorder[rval$lopt]: 15 linear dependencies found
## Reordering variables and trying again:
## Warning in rval$lopt[] <- rval$vorder[rval$lopt]: number of items to replace is
## not a multiple of replacement length
# Find optimal models
for(.x in 1:2) {
  num_variables = 1:length(summary(model[[.x]])$rss)
  # R^2
  plot_RSQ = ggplot(data = data.frame(summary(model[[.x]])$rsq),
                    aes(x = num_variables, y = summary(model[[.x]])$rsq)) +
    geom_line() +
    geom_point(x = which.max(summary(model[[.x]])$rsq),
               y = max(summary(model[[.x]])$rsq), aes(color = "red"),
               show.legend = FALSE) +
    xlab("# Variables") +
    ylab("R-squared") +
    theme_bw()
  # RSS
  plot_RSS = ggplot(data = data.frame(summary(model[[.x]])$rss),
                    aes(x = num_variables, y = summary(model[[.x]])$rss)) +
    geom_line() +
    geom_point(x = which.min(summary(model[[.x]])$rss),
               y = min(summary(model[[.x]])$rss), aes(color = "red"),
               show.legend = FALSE) +
    xlab("# Variables") +
    ylab("RSS") +
    theme_bw()
  # BIC
  plot_BIC = ggplot(data = data.frame(summary(model[[.x]])$bic),
                    aes(x = num_variables, y = summary(model[[.x]])$bic)) +
    geom_line() +
    geom_point(x = which.min(summary(model[[.x]])$bic),
               y = min(summary(model[[.x]])$bic), aes(color = "red"),
               show.legend = FALSE) +
    xlab("# Variables") +
    ylab("BIC") +
    ggtitle("BIC", 
            str_c("Optimal value at ", which.min(summary(model[[.x]])$bic))) + 
    theme_bw()
  # AIC
  plot_AIC = ggplot(data = data.frame(summary(model[[.x]])$cp),
                    aes(x = num_variables, y = summary(model[[.x]])$cp)) +
    geom_line() +
    geom_point(x = which.min(summary(model[[.x]])$cp),
               y = min(summary(model[[.x]])$cp), aes(color = "red"),
               show.legend = FALSE) +
    xlab("# Variables") +
    ylab("AIC") +
    ggtitle("AIC", 
            str_c("Optimal value at ", which.min(summary(model[[.x]])$cp))) + 
    theme_bw()
  # Plot
  gridExtra::grid.arrange(plot_RSQ, plot_RSS, plot_AIC, plot_BIC, 
                           ncol = 2, nrow = 2)
}

ii). Predictions of the Optimal Model

# Get predictions from optimal models
model_coef = map(1:2, 
                 ~coef(model[[.x]], which.min(summary(model[[.x]])$bic)))
temp = bind_rows(
  tibble(method = 'forward', var = names(model_coef[[1]]), 
         coef = model_coef[[1]], varmatch = NA_character_),
  tibble(method = 'backward', var = names(model_coef[[2]]), 
         coef = model_coef[[2]], varmatch = NA_character_)
) 

# Try to figure out programmatically which variables are in the models
for(r in 1:nrow(temp)) {
  if(temp$method[r] == 'forward') {
    potential_names = names(housing.factors)[agrepl(names(model_coef[[1]][r]),
                                            names(housing.factors), 
                                            max.distance = 0.3)]
  } else {
    potential_names = names(housing.factors)[agrepl(names(model_coef[[2]][r]),
                                            names(housing.factors),
                                            max.distance = 0.3)]
  }
  if(length(potential_names) == 0) {
    varmatch = NA_character_
  } else if(length(potential_names) == 1) {
    varmatch = potential_names
  } else {
    varmatch = str_flatten(
      intersect(
        unlist(strsplit(potential_names, '')), 
        unlist(strsplit(potential_names, ''))
      )
    )
  }
  temp$varmatch[r] = varmatch
}

iii). Refitting Forward and Backaward Models

# Refit: Forward
forward_predictors = c('MS.SubClass', 'Lot.Area', 'Lot.Config',
                       'Land.Slope', 'Neighborhood', 'Condition.1',
                       'Condition.2', 'House.Style', 'Overall.Cond',
                       'Year.Built', 'Year.Remod.Add', 'Roof.Style', 
                       'Roof.Matl', 'Exterior.1st', 'Mas.Vnr.Area', 
                       'Exter.Qual', 'Exter.Cond', 'Bsmt.Exposure',
                       'BsmtFin.Type.1', 'BsmtFin.SF.1', 'BsmtFin.SF.2',
                       'Heating.QC', 'Low.Qual.Fin.SF', 'Kitchen.Qual',
                       'TotRms.AbvGrd', 'Functional', 'Fireplace.Qu',
                       'Garage.Type', 'Garage.Yr.Blt', 'Garage.Cond',
                       'Paved.Drive', 'Wood.Deck.SF', 'Misc.Feature',
                       'Misc.Val', 'Yr.Sold', 'Sale.Type',
                       'BsmtFin.Type.1', 'Kitchen.Qual', 'Garage.Cond')
forward_pred = predict(
  lm(formula(paste('SalePrice ~', str_flatten(forward_predictors, "+"))), 
     data = housing.factors), #[housing$Yr.Sold != 2010, ]),
  housing.factors[housing.factors$Yr.Sold == 2010, ]
)

# Refit: Backward
backward_predictors = c('MS.SubClass', 'Lot.Area', 'Land.Slope',
                        'Neighborhood', 'Condition.1', 'Condition.2',
                        'Bldg.Type', 'Overall.Cond', 'Year.Built',
                        'Year.Remod.Add', 'Roof.Style', 'Roof.Matl', 
                        'Exterior.1st', 'Mas.Vnr.Type', 'Exter.Qual', 
                        'Exter.Cond', 'Bsmt.Cond', 'BsmtFin.Type.1', 
                        'BsmtFin.SF.1', 'BsmtFin.SF.1', 'Heating.QC',
                        'Kitchen.Qual', 'Functional', 'Fireplaces',
                        'Fireplace.Qu', 'Garage.Type', 'Garage.Yr.Blt',
                        'Wood.Deck.SF', 'X3Ssn.Porch', 'Screen.Porch',
                        'Misc.Feature', 'Sale.Type', 'BsmtFin.Type.1',
                        'Garage.Cond')
backward_pred = predict(
  lm(formula(paste('SalePrice ~', str_flatten(backward_predictors, "+"))), 
     data = housing.factors), #[housing$Yr.Sold != 2010, ]),
  housing.factors[housing.factors$Yr.Sold == 2010, ]
)
## Warning in predict.lm(lm(formula(paste("SalePrice ~",
## str_flatten(backward_predictors, : prediction from a rank-deficient fit may be
## misleading

b). Generalized Linear Model

# GLM
glm = glm(SalePrice ~ ., data = housing.factors[housing.factors$Yr.Sold != 2010, ])
names(coef(glm)[coef(summary(glm))[, "Pr(>|t|)"]  < 0.05])[-1]
##  [1] "MS.SubClass120"      "MS.SubClass160"      "MS.SubClass180"     
##  [4] "Lot.Area"            "Land.ContourHLS"     "Land.ContourLvl"    
##  [7] "Lot.ConfigCulDSac"   "Land.SlopeMod"       "Land.SlopeSev"      
## [10] "NeighborhoodEdwards" "NeighborhoodGrnHill" "NeighborhoodMitchel"
## [13] "NeighborhoodNAmes"   "NeighborhoodNoRidge" "NeighborhoodNridgHt"
## [16] "NeighborhoodNWAmes"  "NeighborhoodStoneBr" "Condition.1Norm"    
## [19] "Condition.1PosA"     "Condition.1PosN"     "Condition.2PosA"    
## [22] "Condition.2PosN"     "House.StyleSLvl"     "Overall.Qual"       
## [25] "Overall.Cond"        "Year.Built"          "Roof.StyleShed"     
## [28] "Roof.MatlCompShg"    "Roof.MatlMembran"    "Roof.MatlMetal"     
## [31] "Roof.MatlRoll"       "Roof.MatlTar&Grv"    "Roof.MatlWdShake"   
## [34] "Exterior.1stBrkComm" "Exterior.1stPlywood" "Mas.Vnr.TypeBrkCmn" 
## [37] "Mas.Vnr.TypeNone"    "Mas.Vnr.TypeStone"   "Mas.Vnr.Area"       
## [40] "Bsmt.CondGd"         "Bsmt.CondEx"         "Bsmt.ExposureDNE"   
## [43] "Bsmt.ExposureMn"     "BsmtFin.Type.1GLQ"   "BsmtFin.SF.1"       
## [46] "BsmtFin.Type.2GLQ"   "BsmtFin.Type.2LwQ"   "ElectricalFuseA"    
## [49] "ElectricalFuseF"     "ElectricalFuseP"     "X1st.Flr.SF"        
## [52] "Low.Qual.Fin.SF"     "Gr.Liv.Area"         "Full.Bath"          
## [55] "Kitchen.AbvGr"       "FunctionalMaj2"      "FunctionalMin1"     
## [58] "FunctionalMod"       "FunctionalSal"       "FunctionalSev"      
## [61] "Fireplace.QuPo"      "Fireplace.QuGd"      "Garage.TypeDetchd"  
## [64] "Garage.TypeDNE"      "Garage.Yr.Blt"       "Garage.FinishFin"   
## [67] "Garage.FinishRFn"    "Garage.FinishUnf"    "Garage.Cars"        
## [70] "Garage.Area"         "Garage.QualPo"       "Garage.QualFa"      
## [73] "Garage.QualEx"       "Garage.CondGd"       "Open.Porch.SF"      
## [76] "Pool.QCFa"           "Sale.TypeConLI"      "Sale.TypeCWD"

c). Lasso Model

# Lasso [Primary]
# Define x and y objects for Lasso, as well as specifying training data
train = which(housing.factors$Yr.Sold != 2010)
x = model.matrix(SalePrice ~ ., housing.factors)[, -1]
y = housing.factors$SalePrice

# Fit and plot model
lasso_model = cv.glmnet(x[train, ], y[train] , alpha = 1)
plot(lasso_model)

i). Minimun Lambda and 1SE Value

# Find min and 1SE values of lambda
lasso_model$lambda.min; lasso_model$lambda.1se
## [1] 894.4321
## [1] 5238.707
lasso_pred = predict(lasso_model, s = lasso_model$lambda.1se, 
                     newx = x[-train, ])

ii). Refit Lasso Model and Find Non-Zero Coefficients

# Refit model and find non-zero coefficients
lasso_model_coef = map(
  .x = c(lasso_model$lambda.min, lasso_model$lambda.min),
  .f = ~predict(glmnet(x, y ,alpha = 1), s = .x, type = 'coefficients')
)

d). Tree-based and Boosted Models

boost_model = gbm(SalePrice ~ ., 
                  data = mutate_if(housing.factors, is.character, as.factor)[housing.factors$Yr.Sold != 2010, ],
                  distribution = 'gaussian', 
                  n.trees = 5000,
                  cv.folds = 10,
                  shrinkage = 0.1,
                  interaction.depth = 4)

i). Summary Table of Boosted Model

kable(summary(boost_model))

var rel.inf
Overall.Qual Overall.Qual 36.1225582
Neighborhood Neighborhood 13.9607600
Gr.Liv.Area Gr.Liv.Area 12.0516750
Total.Bsmt.SF Total.Bsmt.SF 5.4751502
Garage.Cars Garage.Cars 4.2847963
BsmtFin.SF.1 BsmtFin.SF.1 2.8097106
X1st.Flr.SF X1st.Flr.SF 2.6999941
Bsmt.Qual Bsmt.Qual 2.4312822
Lot.Area Lot.Area 2.1808841
Kitchen.Qual Kitchen.Qual 1.3982185
X2nd.Flr.SF X2nd.Flr.SF 1.3190088
Mas.Vnr.Area Mas.Vnr.Area 0.9747818
Fireplace.Qu Fireplace.Qu 0.9523285
Year.Remod.Add Year.Remod.Add 0.9102636
MS.SubClass MS.SubClass 0.8173353
Bsmt.Unf.SF Bsmt.Unf.SF 0.8001554
Garage.Area Garage.Area 0.7872271
Sale.Condition Sale.Condition 0.7651695
Garage.Type Garage.Type 0.7276290
Overall.Cond Overall.Cond 0.6813413
Lot.Frontage Lot.Frontage 0.5662562
Exterior.1st Exterior.1st 0.5531077
Exterior.2nd Exterior.2nd 0.4858263
Open.Porch.SF Open.Porch.SF 0.4533702
ï..Order ï..Order 0.4168310
Bsmt.Exposure Bsmt.Exposure 0.3982085
BsmtFin.Type.1 BsmtFin.Type.1 0.3802796
Year.Built Year.Built 0.3092281
Screen.Porch Screen.Porch 0.2981263
Full.Bath Full.Bath 0.2774098
Mo.Sold Mo.Sold 0.2674758
Wood.Deck.SF Wood.Deck.SF 0.2526765
Fireplaces Fireplaces 0.2447132
PID PID 0.2121238
Condition.1 Condition.1 0.2022421
Garage.Yr.Blt Garage.Yr.Blt 0.1906354
Central.Air Central.Air 0.1747540
Sale.Type Sale.Type 0.1732011
Mas.Vnr.Type Mas.Vnr.Type 0.1492795
TotRms.AbvGrd TotRms.AbvGrd 0.1470061
Functional Functional 0.1427143
Roof.Matl Roof.Matl 0.1263476
Lot.Config Lot.Config 0.1231453
Land.Contour Land.Contour 0.1176316
Bsmt.Full.Bath Bsmt.Full.Bath 0.1020748
House.Style House.Style 0.0675096
Heating.QC Heating.QC 0.0633526
Bedroom.AbvGr Bedroom.AbvGr 0.0616296
Enclosed.Porch Enclosed.Porch 0.0614063
Garage.Finish Garage.Finish 0.0604566
Land.Slope Land.Slope 0.0596957
Bsmt.Cond Bsmt.Cond 0.0593238
Garage.Cond Garage.Cond 0.0547404
BsmtFin.Type.2 BsmtFin.Type.2 0.0535483
Condition.2 Condition.2 0.0496386
Exter.Qual Exter.Qual 0.0494800
Roof.Style Roof.Style 0.0460229
Half.Bath Half.Bath 0.0453486
X3Ssn.Porch X3Ssn.Porch 0.0453451
Lot.Shape Lot.Shape 0.0410120
Garage.Qual Garage.Qual 0.0306597
Alley Alley 0.0255183
Exter.Cond Exter.Cond 0.0251966
BsmtFin.SF.2 BsmtFin.SF.2 0.0239556
MS.Zoning MS.Zoning 0.0237280
Foundation Foundation 0.0211307
Fence Fence 0.0203420
Misc.Val Misc.Val 0.0202177
Low.Qual.Fin.SF Low.Qual.Fin.SF 0.0169254
Bsmt.Half.Bath Bsmt.Half.Bath 0.0137945
Electrical Electrical 0.0129283
Bldg.Type Bldg.Type 0.0108335
Paved.Drive Paved.Drive 0.0100138
Yr.Sold Yr.Sold 0.0039051
Misc.Feature Misc.Feature 0.0038024
Kitchen.AbvGr Kitchen.AbvGr 0.0021680
Heating Heating 0.0014357
Street Street 0.0000000
Utilities Utilities 0.0000000
Pool.Area Pool.Area 0.0000000
Pool.QC Pool.QC 0.0000000

ii). Relative Influence Chart

for(.x in 1:5) {
  plot(boost_model, i = summary(boost_model)[.x, 'var'])
}

boost_pred = predict(boost_model, 
                     newdata = housing.factors[housing.factors$Yr.Sold == 2010, ],
                     n.trees = 5000)
## Warning in predict.gbm(boost_model, newdata =
## housing.factors[housing.factors$Yr.Sold == : NAs introduced by coercion

3. Performance Evaluation

a). Performance Metrics Function

# Create performance_metrics function
performance_metrics = function(actual = housing.factors[housing.factors$Yr.Sold == 2010, 'SalePrice'], predicted, plot = T, by_neighborhood = F) {
  # Check that actual and predicted values are the same length
  if(length(actual) != length(predicted)) {
    message("'actual' and 'predicted' vectors must be the same length.")
  } else {
    # Compute metrics (MSE, RMSE, MAE, relative error)
    # Including by neighborhood
    if(by_neighborhood) {
      metrics = tibble(
        neighborhood = housing.factors[housing.factors$Yr.Sold == 2010, 'Neighborhood'],
        actual = actual,
        predicted = as.numeric(predicted),
        mse = (actual - predicted)^2,
        mae = abs(actual - predicted),
        rel_error = (predicted - actual) / actual
      ) %>% 
        group_by(neighborhood) %>% 
        summarize(across(mse:rel_error, mean)) %>% 
        ungroup()
      
      # Plot
      barplot = ggplot(data = pivot_longer(metrics, cols = mse:rel_error,
                                           names_to = 'performance_metric',
                                           values_to = 'metric_score'),
                    aes(x = performance_metric, y = metric_score)) + 
        geom_bar(stat = 'identity') + 
        geom_text(aes(label = round(metric_score, 3))) + 
        xlab("Metric") +
        ylab("Score") + 
        facet_wrap(~neighborhood) + 
        theme_bw()
      scatter = ggplot(data = tibble(
        neighborhood = housing.factors[housing.factors$Yr.Sold == 2010, 'Neighborhood'],
        actual = actual, 
        predicted = predicted), 
        aes(x = actual, y = predicted)) + 
        geom_point(aes(size = abs(actual - predicted)), alpha = 0.4) + 
        xlab("Actual") + 
        ylab("Predicted") + 
        facet_wrap('neighborhood') +
        geom_abline(slope = 1, intercept = 0, col = 'red') + 
        theme_bw()
    } else {
      # Compute error and create data frame
      mse = mean((actual - predicted)^2)
      mae = mean(abs(actual - predicted))
      rel_error = mean((predicted - actual) / actual)
      metrics = tibble(mse = mse, mae = mae, rel_error = rel_error)
      
      # Plot
      barplot = ggplot(data = tibble(mse, mae, rel_error) %>% 
                      pivot_longer(cols = everything(),
                                   names_to = 'performance_metric',
                                   values_to = 'metric_score'),
                    aes(x = performance_metric, y = metric_score)) + 
        geom_bar(stat = 'identity') + 
        geom_text(aes(label = round(metric_score, 3))) + 
        xlab("Metric") +
        ylab("Score") + 
        theme_bw()
      scatter = ggplot(data = tibble(actual = actual, 
                                     predicted = predicted), 
                       aes(x = actual, y = predicted)) + 
        geom_point(aes(size = abs(actual - predicted)), alpha = 0.4) + 
        xlab("Actual") + 
        ylab("Predicted") + 
        geom_abline(slope = 1, intercept = 0, col = 'red') + 
        theme_bw()
    }
    
    # Return objects
    if(plot) {
      return(list(metrics = metrics, barplot = barplot, scatter = scatter))
    } else {
      return(list(metrics = metrics))
    }
  }
}

b). Comparing Accuracy of Prediction Estimates Against Actual Values in 2010.

# Use performance_metrics function defined above for all models
map(list(forward_pred = forward_pred, backward_pred = backward_pred,
         lasso_pred = lasso_pred, boost_pred = boost_pred),
    ~performance_metrics(predicted = .x))
## $forward_pred
## $forward_pred$metrics
## # A tibble: 1 x 3
##          mse    mae rel_error
##        <dbl>  <dbl>     <dbl>
## 1 604242156. 18025.    0.0186
## 
## $forward_pred$barplot

## 
## $forward_pred$scatter

## 
## 
## $backward_pred
## $backward_pred$metrics
## # A tibble: 1 x 3
##          mse    mae rel_error
##        <dbl>  <dbl>     <dbl>
## 1 696652643. 18607.    0.0317
## 
## $backward_pred$barplot

## 
## $backward_pred$scatter

## 
## 
## $lasso_pred
## $lasso_pred$metrics
## # A tibble: 1 x 3
##          mse    mae rel_error
##        <dbl>  <dbl>     <dbl>
## 1 863799315. 20212.    0.0552
## 
## $lasso_pred$barplot

## 
## $lasso_pred$scatter

## 
## 
## $boost_pred
## $boost_pred$metrics
## # A tibble: 1 x 3
##           mse    mae rel_error
##         <dbl>  <dbl>     <dbl>
## 1 1047425367. 23285.    0.0965
## 
## $boost_pred$barplot

## 
## $boost_pred$scatter

c). Home Features Relation to the Model

i). Home Features That are Most Predictive of Sales Price.

#Code Here

ii). How do the Above Features Relate to Sales Price?

#Code Here

4. The Model’s accuracy accros Neighbourhoods

# TODO: Khadija, the code below calls the performance_metrics function and should help
map(list(forward_pred = forward_pred, backward_pred = backward_pred,
         lasso_pred = lasso_pred, boost_pred = boost_pred),
    ~performance_metrics(predicted = .x, by_neighborhood = T))
## `summarise()` ungrouping output (override with `.groups` argument)
## `summarise()` ungrouping output (override with `.groups` argument)
## `summarise()` ungrouping output (override with `.groups` argument)
## `summarise()` ungrouping output (override with `.groups` argument)
## $forward_pred
## $forward_pred$metrics
## # A tibble: 25 x 4
##    neighborhood         mse    mae rel_error
##    <chr>              <dbl>  <dbl>     <dbl>
##  1 Blmngtn       534641678. 18275.  -0.0973 
##  2 Blueste        62365813.  7896.  -0.00388
##  3 BrDale         76144821.  7623.   0.0439 
##  4 BrkSide       232700982. 12629.   0.0324 
##  5 ClearCr      1388209494. 28032.  -0.0927 
##  6 CollgCr       428056395. 16685.  -0.0365 
##  7 Crawfor       752282643. 20919.  -0.0494 
##  8 Edwards       571851979. 18466.   0.0297 
##  9 Gilbert       470414307. 15653.  -0.0364 
## 10 Greens        290576768. 15101.   0.0568 
## # ... with 15 more rows
## 
## $forward_pred$barplot

## 
## $forward_pred$scatter

## 
## 
## $backward_pred
## $backward_pred$metrics
## # A tibble: 25 x 4
##    neighborhood         mse    mae rel_error
##    <chr>              <dbl>  <dbl>     <dbl>
##  1 Blmngtn        86104575.  7844.   -0.0424
##  2 Blueste        20518623.  3285.   -0.0202
##  3 BrDale         21323671.  3738.    0.0134
##  4 BrkSide       335128674. 15229.    0.0545
##  5 ClearCr      1305041158. 22983.   -0.0821
##  6 CollgCr       628532670. 19066.   -0.0347
##  7 Crawfor       913663000. 24105.   -0.0505
##  8 Edwards       522259464. 15617.    0.0219
##  9 Gilbert       364965329. 17400.   -0.0146
## 10 Greens        418391635. 19308.    0.0536
## # ... with 15 more rows
## 
## $backward_pred$barplot

## 
## $backward_pred$scatter

## 
## 
## $lasso_pred
## $lasso_pred$metrics
## # A tibble: 25 x 4
##    neighborhood         mse    mae rel_error
##    <chr>              <dbl>  <dbl>     <dbl>
##  1 Blmngtn       345460431. 18339.    0.107 
##  2 Blueste       819529315. 27410.    0.162 
##  3 BrDale        895053251. 27430.    0.295 
##  4 BrkSide       102904828.  8033.    0.0375
##  5 ClearCr      1084801731. 27615.   -0.0928
##  6 CollgCr       267557593. 13204.   -0.0414
##  7 Crawfor      2208607219. 42151.   -0.120 
##  8 Edwards       795228646. 21224.    0.0941
##  9 Gilbert       507567473. 17836.   -0.0118
## 10 Greens        656537098. 22369.    0.136 
## # ... with 15 more rows
## 
## $lasso_pred$barplot

## 
## $lasso_pred$scatter

## 
## 
## $boost_pred
## $boost_pred$metrics
## # A tibble: 25 x 4
##    neighborhood         mse    mae rel_error
##    <chr>              <dbl>  <dbl>     <dbl>
##  1 Blmngtn        11270936.  3345.    0.0190
##  2 Blueste       372515068. 16374.    0.0985
##  3 BrDale        830366856. 28081.    0.298 
##  4 BrkSide       486317796. 19228.    0.175 
##  5 ClearCr      1667238653. 31689.   -0.0927
##  6 CollgCr       368467122. 14856.   -0.0336
##  7 Crawfor      2041202625. 38646.   -0.137 
##  8 Edwards      1167985791. 29895.    0.247 
##  9 Gilbert       365224202. 16310.   -0.0495
## 10 Greens        241627717. 13443.    0.0549
## # ... with 15 more rows
## 
## $boost_pred$barplot

## 
## $boost_pred$scatter

5. Renovation Value Calculator (Evan and Anthony)

I am going to write a bit about the calculator

What it does

Data sources:

Room Renovation Costs Business Insider

Roof Renovation Cost Super Storm Restoration

reno_value = function(upgrade = c('add_full_bathroom', 'remodel_kitchen',
                                  'finish_basement', 'replace_roof'),
                      budget = c('medium', 'low', 'high')) {

  # # Confirm upgrade and budget args; otherwise throw an error
  upgrade = tryCatch(
    match.arg(upgrade, choices = c('add_bathroom', 'remodel_kitchen',
                                  'finish_basement', 'replace_roof'),
                      several.ok = T),
    error = identity
  )
  budget = tryCatch(
    match.arg(budget, choices = c('low', 'medium', 'high'), several.ok = F),
    error = identity
  )
  
  # Handle errors
  if(str_detect(upgrade, "Error") | str_detect(budget, "Error")) {
      suppressWarnings(return(message(upgrade)))
      break()
  } else {
    # Update data based on stated upgrades
    remodeled_housing = mutate(housing, Reno.Cost = 0)
    
    # Add bathroom
    if('add_full_bathroom' %in% upgrade) {
      remodeled_housing = mutate(
        remodeled_housing,
        budget = budget,
        Reno.Cost = case_when(
          budget == 'low' ~ Reno.Cost + 5957,
          budget == 'medium' ~ Reno.Cost + 10349,
          budget == 'high' ~ Reno.Cost + 14833,
          T ~ Reno.Cost
        ),
        Full.Bath = Full.Bath + 1,
        Year.Remod.Add = 2010
      )
    }
    
    # Remodel kitchen
    if('remodel_kitchen' %in% upgrade) {
      message('Note: Remodeling kitchens that are already of excellent quality (i.e., "Ex") will not increase the estimated sale price.')
      remodeled_housing = mutate(
        remodeled_housing,
        Reno.Cost = case_when(
          Kitchen.Qual == 'Ex' ~ Reno.Cost,
          budget == 'low' ~ Reno.Cost + 12557,
          budget == 'medium' ~ Reno.Cost + 23556,
          budget == 'high' ~ Reno.Cost + 34789,
          T ~ Reno.Cost
        ),
        Kitchen.Qual = case_when(
          Kitchen.Qual == 'Gd' ~ 'Ex',
          Kitchen.Qual == "TA" & budget == 'low' ~ 'Gd',
          Kitchen.Qual == "TA" ~ 'Ex',
          Kitchen.Qual == 'Fa' & budget == 'low' ~ "TA",
          Kitchen.Qual == 'Fa' & budget == 'medium' ~ "Gd",
          Kitchen.Qual == 'Fa' & budget == 'high' ~ 'Ex',
          Kitchen.Qual == 'Po' & budget == 'low' ~ 'Fa',
          Kitchen.Qual == 'Po' & budget == 'medium' ~ "TA",
          Kitchen.Qual == 'Po' & budget == 'high' ~ 'Gd',
          T ~ Kitchen.Qual
        ),
        Year.Remod.Add = 2010
      )
    }
    
    # Finish basement
    if('finish_basement' %in% upgrade) {
      message('Note: Properties without a basement obviously cannot have finished basements, so this renovation will not increase their estimated sale price.')
      remodeled_housing = mutate(
        remodeled_housing,
        Reno.Cost = case_when(
          Bsmt.Cond %in% c("DNE", '') ~ Reno.Cost,
          budget == 'low' ~ Reno.Cost + 0.75 * 15000,
          budget == 'medium' ~ Reno.Cost + 15000,
          budget == 'high' ~ Reno.Cost + 1.25 * 15000,
          T ~ Reno.Cost
        ),
        BsmtFin.Type.1 = case_when(
          Bsmt.Cond %in% c("DNE", '') ~ BsmtFin.Type.1,
          budget == 'low' ~ "BLQ",
          budget == 'medium' ~ "ALQ",
          budget == 'high' ~ "GLQ",
          T ~ BsmtFin.Type.1
        ),
        BsmtFin.SF.1 = BsmtFin.SF.1 + Bsmt.Unf.SF,
        Year.Remod.Add = 2010
      )
    }
    
    # Replace roof
    if('replace_roof' %in% upgrade) {
      remodeled_housing = mutate(
        remodeled_housing,
        Reno.Cost = case_when(
          budget == 'low' ~ Reno.Cost + 5100,
          budget == 'medium' ~ Reno.Cost + 10000,
          budget == 'high' ~ Reno.Cost + 15000,
          T ~ Reno.Cost
        ),
        Exter.Cond = case_when(
          Exter.Cond == 'Gd' ~ 'Ex',
          Exter.Cond == "TA" & budget == 'low' ~ 'Gd',
          Exter.Cond == "TA" ~ 'Ex',
          Exter.Cond == "Fa" & budget == 'low' ~ "TA",
          Exter.Cond == "Fa" & budget == 'medium' ~ 'Gd',
          Exter.Cond == "Fa" & budget == 'high' ~ 'Ex',
          Exter.Cond == "Po" & budget == 'low' ~ "Fa",
          Exter.Cond == "Po" & budget == 'medium' ~ "TA",
          Exter.Cond == "Po" & budget == 'high' ~ 'Gd',
          T ~ Exter.Cond
        ),
        Year.Remod.Add = 2010
      )
    }
    
    # Predict based on new features
    costs_benefits = tibble(
      orig_predicted_sale_price = as.numeric(lasso_pred),
      new_predicted_sale_price = predict(
        boost_model, 
        newdata = remodeled_housing[remodeled_housing$Yr.Sold == 2010, ],
        n.trees = 5000
      ),
      remodeling_costs = remodeled_housing[remodeled_housing$Yr.Sold == 2010,
                                           'Reno.Cost'],
      net = new_predicted_sale_price - orig_predicted_sale_price - remodeling_costs
    ) 
    
    # Return costs and predictions
    # return(list(remodeled_housing = remodeled_housing,
    #             costs_benefits = costs_benefits))
    
    
    
    if('add_full_bathroom' %in% upgrade) {
        return(kable(list("remodeled_housing" =
                          remodeled_housing[c("ï..Order", "PID", "Full.Bath",
                                            "Year.Remod.Add", "SalePrice",
                                            "Reno.Cost")],
                          "cost_benefits" = costs_benefits)))
    } else if ('remodel_kitchen' %in% upgrade){
        return(kable(list("remodeled_housing"=
                          remodeled_housing[c("ï..Order", "PID", "Kitchen.Qual",
                                            "Year.Remod.Add", "SalePrice",
                                            "Reno.Cost")],
                          "cost_benefits" = costs_benefits)))
    } else if ('finish_basement' %in% upgrade){
        return(kable(list("remodeled_housing"=
                          remodeled_housing[c("ï..Order", "PID", "BsmtFin.SF.1",
                                            "Year.Remod.Add", "SalePrice",
                                            "Reno.Cost")],
                          "cost_benefits" = costs_benefits)))
    } else if('replace_roof' %in% upgrade) {
        return(kable(list("remodeled_housing"=
                          remodeled_housing[c("ï..Order", "PID", "Exter.Cond",
                                            "Year.Remod.Add", "SalePrice",
                                            "Reno.Cost")],
                          "cost_benefits" = costs_benefits)))
    } else{
        return(kable(list("remodeled_housing"=
                        remodeled_housing[c("ï..Order", "PID", "Full.Bath",
                                            "Kitchen.Qual", "BsmtFin.SF.1",
                                            "Exter.Cond", "Year.Remod.Add",
                                            "SalePrice", "Reno.Cost")],
                        "cost_benefits" = costs_benefits)))      
    }
                                  
           
  }
}

Using the Renovation Calculator

reno_value('add_bathroom', 'high')
## Warning in predict.gbm(boost_model, newdata =
## remodeled_housing[remodeled_housing$Yr.Sold == : NAs introduced by coercion
ï..Order PID Full.Bath Kitchen.Qual BsmtFin.SF.1 Exter.Cond Year.Remod.Add SalePrice Reno.Cost
1 526301100 1 TA 639 TA 1960 215000 0
2 526350040 1 TA 468 TA 1961 105000 0
3 526351010 1 Gd 923 TA 1958 172000 0
4 526353030 2 Ex 1065 TA 1968 244000 0
5 527105010 2 TA 791 TA 1998 189900 0
6 527105030 2 Gd 602 TA 1998 195500 0
7 527127150 2 Gd 616 TA 2001 213500 0
8 527145080 2 Gd 263 TA 1992 191500 0
9 527146030 2 Gd 1180 TA 1996 236500 0
10 527162130 2 Gd 0 TA 1999 189000 0
11 527163010 2 TA 0 TA 1994 175900 0
12 527165230 2 TA 935 Gd 2007 185000 0
13 527166040 2 TA 0 TA 1998 180400 0
14 527180040 1 Gd 637 TA 1990 171500 0
15 527182190 1 Gd 368 TA 1985 212000 0
16 527216070 3 Ex 1416 TA 2003 538000 0
17 527225035 2 TA 427 TA 2005 164000 0
18 527258010 1 Ex 1445 TA 2010 394432 0
19 527276150 1 TA 120 TA 1951 141000 0
20 527302110 2 TA 790 TA 1988 210000 0
21 527358140 2 TA 705 TA 1977 190000 0
22 527358200 2 Gd 885 TA 1974 170000 0
23 527368020 2 Gd 533 TA 2000 216000 0
24 527402200 1 TA 578 TA 1970 149000 0
25 527402250 1 TA 734 TA 2008 149900 0
26 527403020 1 TA 775 TA 1968 142000 0
27 527404120 1 TA 804 TA 1970 126000 0
28 527425090 1 TA 432 TA 1971 115000 0
29 527427230 2 Gd 1051 TA 1999 184000 0
30 527451180 1 TA 156 TA 1971 96000 0
31 527451330 1 TA 300 TA 1971 105500 0
32 527451410 1 TA 0 TA 1971 88000 0
33 527452190 2 TA 360 TA 1977 127500 0
34 527453130 2 Gd 514 TA 1975 149900 0
35 527453150 1 TA 0 TA 1975 120000 0
36 527454200 2 TA 311 TA 1978 146000 0
37 528108120 2 Ex 0 TA 2010 376162 0
38 528112020 2 Gd 1218 TA 2008 306000 0
39 528120060 2 Ex 1646 TA 2010 395192 0
40 528120090 2 Gd 0 TA 2010 290941 0
41 528120100 2 Gd 1201 TA 2005 220000 0
42 528120120 2 Ex 110 TA 2005 275000 0
43 528138020 2 Ex 28 TA 2006 259000 0
44 528138060 2 Gd 2 TA 2004 214000 0
45 528150070 2 Ex 2188 TA 2010 611657 0
46 528175010 2 Gd 733 TA 2010 224000 0
47 528176010 2 Ex 1373 TA 2004 500000 0
48 528176070 2 Gd 578 TA 2002 320000 0
49 528180070 2 Ex 456 TA 2005 319900 0
50 528181050 2 Gd 24 TA 2006 205000 0
51 528188120 2 Gd 0 TA 2003 175500 0
52 528218150 2 Gd 0 TA 2005 199500 0
53 528228285 2 Gd 16 TA 2006 160000 0
54 528228440 2 Gd 24 TA 2005 192000 0
55 528231020 2 Gd 326 TA 2004 184500 0
56 528240070 2 Gd 625 TA 2002 216500 0
57 528240130 2 Gd 0 TA 2004 185088 0
58 528250100 2 TA 250 TA 2000 180000 0
59 528292020 2 Gd 0 TA 2001 222500 0
60 528328100 2 Gd 0 TA 1999 333168 0
61 528344070 2 Gd 0 TA 1998 355000 0
62 528358010 2 Gd 919 TA 1996 260400 0
63 528363130 2 Gd 1032 TA 1995 325000 0
64 528382020 2 Gd 524 TA 2007 290000 0
65 528382030 2 TA 0 TA 1998 221000 0
66 528386040 2 Gd 816 TA 1996 410000 0
67 528445060 2 Gd 0 TA 2006 221500 0
68 528456160 2 Gd 0 TA 2010 204500 0
69 528458070 2 Gd 24 TA 2009 215200 0
70 528458110 2 Gd 1078 TA 2008 262500 0
71 528477080 2 Gd 222 TA 2005 254900 0
72 528480090 2 Gd 1414 TA 2005 271500 0
73 531367050 2 Gd 656 TA 2004 233000 0
74 531369060 2 Gd 0 TA 2004 181000 0
75 531380080 2 Gd 695 TA 2002 205000 0
76 531451110 2 TA 543 TA 1980 143000 0
77 531451280 2 Gd 0 TA 1992 189000 0
78 531452020 2 TA 0 TA 1979 99500 0
79 531452050 1 TA 623 TA 1984 125000 0
80 531452180 2 Gd 402 TA 2003 194500 0
81 531453010 2 TA 338 TA 1985 152000 0
82 531453040 2 TA 0 TA 1981 171000 0
83 531477050 1 TA 0 Fa 1950 67500 0
84 532351140 2 TA 0 TA 1978 112000 0
85 532354090 1 Gd 899 TA 1995 148000 0
86 532376160 1 TA 553 Gd 2009 138500 0
87 532377060 1 TA 450 Gd 1967 122000 0
88 532377100 1 TA 824 TA 1963 133000 0
89 532378110 1 TA 659 Gd 2010 127000 0
90 532479070 2 TA 126 Gd 2002 169000 0
91 533130020 2 Gd 674 TA 1992 190000 0
92 533130130 2 Gd 250 TA 1993 362500 0
93 533130160 2 Gd 1129 TA 1993 285000 0
94 533205060 2 Gd 1298 TA 2005 260000 0
95 533208090 2 Gd 0 TA 2004 190000 0
96 533210060 2 Gd 280 TA 2004 155000 0
97 533212010 2 Gd 0 TA 2005 151000 0
98 533212020 2 Gd 368 TA 2005 149500 0
99 533212060 2 Gd 376 TA 2005 152000 0
100 533213030 2 Gd 578 TA 2009 222000 0
101 533221090 2 Gd 378 TA 2000 177500 0
102 533221110 2 Gd 466 TA 2000 177000 0
103 533223020 2 Gd 604 TA 1999 155000 0
104 533223100 2 Gd 244 TA 2003 147110 0
105 533238045 1 Gd 1032 TA 2010 267916 0
106 533244030 2 Gd 484 TA 2000 254000 0
107 533253060 1 Gd 728 TA 1980 155000 0
108 533253210 1 Gd 1052 TA 1978 206000 0
109 533352170 2 Gd 533 TA 2005 130500 0
110 534102025 2 Gd 833 TA 2002 230000 0
111 534129040 2 TA 506 TA 1967 218500 0
112 534151175 2 Gd 1137 TA 1993 243500 0
113 534152050 2 Gd 1200 TA 2001 205000 0
114 534152070 3 TA 687 TA 1978 212500 0
115 534152100 2 TA 394 TA 1988 196500 0
116 534176060 1 Gd 982 TA 2006 197500 0
117 534176230 1 TA 329 TA 1971 171000 0
118 534202160 1 TA 698 TA 1966 142250 0
119 534251320 1 TA 569 TA 1963 143000 0
120 534276360 1 TA 569 TA 1959 128950 0
121 534401110 1 TA 1059 TA 1966 159000 0
122 534401140 2 Gd 1010 TA 1967 178900 0
123 534403360 2 TA 0 TA 1964 136300 0
124 534403410 1 TA 1014 TA 1964 180500 0
125 534425310 1 Gd 763 Gd 1963 137500 0
126 534427010 2 TA 1500 TA 2001 84900 0
127 534430080 1 Gd 49 TA 1996 142125 0
128 534431050 2 TA 670 TA 2002 197600 0
129 534431070 2 TA 300 Gd 1950 172500 0
130 534450180 1 TA 696 Gd 2008 116500 0
131 534451150 1 Fa 0 Po 1966 76500 0
132 534475100 1 TA 354 TA 1954 128000 0
133 534476260 1 TA 674 TA 1972 153000 0
134 534479320 1 TA 540 TA 1954 132000 0
135 535101020 1 Gd 944 TA 2008 178000 0
136 535106190 2 TA 443 TA 1960 154300 0
137 535125010 2 TA 912 TA 1989 180000 0
138 535126040 2 Gd 247 TA 2002 190000 0
139 535152010 2 TA 0 TA 1958 135000 0
140 535152050 2 Gd 1188 TA 2009 214000 0
141 535152130 1 TA 856 TA 1959 136000 0
142 535152150 1 Gd 1018 TA 1959 165500 0
143 535152250 1 TA 922 Gd 1957 145000 0
144 535153070 1 TA 0 TA 1959 148000 0
145 535154050 1 TA 1000 TA 1959 142000 0
146 535175070 1 TA 697 TA 1960 167500 0
147 535175180 1 TA 936 TA 1959 108538 0
148 535179020 1 TA 734 TA 1959 159500 0
149 535180130 1 TA 0 TA 1956 108000 0
150 535302080 1 Fa 339 TA 1952 135000 0
151 535302200 1 TA 648 Gd 1955 122500 0
152 535304060 1 TA 532 TA 1958 119000 0
153 535304180 1 Gd 731 Gd 2007 109000 0
154 535325400 1 TA 0 TA 1994 105000 0
155 535327140 1 TA 0 TA 2007 107500 0
156 535350030 1 TA 320 TA 2003 144900 0
157 535350040 1 TA 248 TA 2000 129000 0
158 535353190 1 TA 0 TA 1950 97500 0
159 535377090 0 TA 1056 TA 1980 144000 0
160 535401080 1 Gd 72 Gd 2006 162000 0
161 535425010 2 Gd 0 Gd 2007 242000 0
162 535450210 1 TA 481 TA 2004 132000 0
163 535453070 1 Gd 340 TA 1994 154000 0
164 535454070 2 TA 507 Fa 1952 166000 0
165 535456110 1 Gd 234 TA 2000 134800 0
166 535457010 1 TA 0 TA 1962 160000 0
167 535457090 1 TA 588 TA 1960 148000 0
168 535476350 1 TA 717 TA 1984 192000 0
169 535477020 1 TA 0 TA 1966 155000 0
170 902102100 1 TA 48 TA 1954 80400 0
171 902104060 1 TA 0 TA 2004 96500 0
172 902106130 1 TA 579 TA 1950 109500 0
173 902106140 1 TA 0 TA 1950 115000 0
174 902110090 1 Gd 274 TA 1957 143000 0
175 902125080 2 TA 0 Gd 1950 107400 0
176 902125160 1 TA 0 Gd 1950 80000 0
177 902128170 1 Gd 510 Gd 1992 119000 0
178 902206040 1 TA 234 TA 2001 130000 0
179 902206130 1 Fa 0 TA 2000 119000 0
180 902206220 1 Gd 780 Gd 2009 129000 0
181 902206240 1 TA 176 TA 1962 100000 0
182 902207130 1 TA 0 Fa 1970 12789 0
183 902207140 1 TA 0 Gd 2003 105900 0
184 902305110 2 Gd 0 Gd 2003 150000 0
185 902327040 2 TA 686 Gd 1950 139000 0
186 902329030 3 Gd 0 Gd 2002 240000 0
187 902401060 2 Fa 0 Fa 1950 76500 0
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2639 902103090 1 Fa 284 TA 1980 111500 0
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2641 902106040 1 Ex 16 TA 1990 178000 0
2642 902106090 1 TA 208 TA 1970 139900 0
2643 902108060 1 Gd 0 TA 1950 105000 0
2644 902109010 1 Gd 0 TA 2005 110000 0
2645 902110120 2 Fa 0 TA 1950 111500 0
2646 902110130 1 TA 143 TA 1950 108000 0
2647 902111010 1 TA 0 TA 1950 111500 0
2648 902125020 1 Ex 0 TA 1991 124000 0
2649 902128020 1 TA 0 TA 1950 105000 0
2650 902128100 1 TA 0 TA 1950 116000 0
2651 902134060 1 TA 0 TA 1950 96900 0
2652 902204060 1 TA 576 TA 1955 135500 0
2653 902204120 1 Gd 0 Gd 1950 139000 0
2654 902206020 1 TA 416 TA 1950 61500 0
2655 902206090 1 TA 310 TA 1950 120000 0
2656 902207080 1 TA 256 Gd 2005 126175 0
2657 902207110 1 Fa 0 TA 1950 64000 0
2658 902301120 2 Fa 0 Fa 1950 137000 0
2659 902305090 2 TA 0 TA 1950 87000 0
2660 902325050 1 TA 390 TA 1970 163000 0
2661 902325100 2 TA 0 TA 2005 155000 0
2662 902325160 1 TA 0 TA 1950 79000 0
2663 902328100 1 TA 0 TA 1950 144000 0
2664 902329070 1 TA 0 TA 1993 114504 0
2665 902329090 1 Gd 0 TA 1950 157000 0
2666 902400090 1 TA 0 TA 1950 125000 0
2667 902400110 2 Ex 0 Gd 1993 475000 0
2668 902401090 2 TA 0 TA 1950 93500 0
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2671 903200050 1 TA 266 TA 1950 100000 0
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2921 923228310 1 TA 252 TA 1970 71000 0
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2927 923276100 1 TA 301 TA 1983 131000 0
2928 923400125 1 TA 337 TA 1992 132000 0
2929 924100070 1 TA 1071 TA 1975 170000 0
2930 924151050 2 TA 758 TA 1994 188000 0
orig_predicted_sale_price new_predicted_sale_price remodeling_costs net
194317.97 149063.4 0 -45254.54948
122603.93 147128.4 0 24524.48025
161698.70 186194.0 0 24495.30398
263650.92 215500.2 0 -48150.69663
168430.92 172015.3 0 3584.36013
185454.87 180924.5 0 -4530.41653
215296.05 199193.2 0 -16102.85410
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238086.01 219660.6 0 -18425.38506
203415.13 190414.7 0 -13000.44478
173248.73 164779.3 0 -8469.39499
166384.75 174940.6 0 8555.89351
166437.97 162661.7 0 -3776.22907
203054.47 176324.1 0 -26730.42061
216521.59 215478.2 0 -1043.39461
360160.09 407835.2 0 47675.10535
213568.39 214372.4 0 804.00142
336451.25 294250.2 0 -42201.03433
99017.48 137292.7 0 38275.20945
214217.65 200945.4 0 -13272.21629
203302.08 188287.0 0 -15015.05132
196813.39 173942.4 0 -22871.03213
204228.21 175002.7 0 -29225.47247
152893.51 156961.3 0 4067.78141
147777.34 163169.9 0 15392.60029
132157.06 157980.0 0 25822.98135
111874.78 145421.4 0 33546.58545
93905.14 141249.9 0 47344.78697
205089.94 190664.9 0 -14425.06452
126022.55 135290.3 0 9267.70837
117179.15 135569.0 0 18389.83709
128588.22 135206.5 0 6618.25409
153535.04 151774.2 0 -1760.85272
170012.43 156828.0 0 -13184.42063
142161.98 142463.8 0 301.78470
165024.43 153499.7 0 -11524.75729
346549.85 291408.6 0 -55141.23424
289590.34 265407.0 0 -24183.31054
349916.80 322136.8 0 -27779.98607
237426.00 228481.3 0 -8944.68181
224464.00 205096.4 0 -19367.62280
317887.12 264704.9 0 -53182.23450
305209.77 234284.5 0 -70925.22817
208815.25 177865.1 0 -30950.18571
394935.42 347698.6 0 -47236.79121
210420.93 193663.5 0 -16757.45573
410220.21 333682.0 0 -76538.18690
280204.48 290914.9 0 10710.44453
322982.86 250184.5 0 -72798.33941
220059.09 202008.6 0 -18050.51950
198479.68 164333.9 0 -34145.74759
175154.11 167784.5 0 -7369.64015
181360.59 162018.2 0 -19342.42268
207318.16 192024.5 0 -15293.62175
187610.09 171255.2 0 -16354.89051
206131.86 192354.3 0 -13777.57839
203043.40 177968.0 0 -25075.41684
180601.43 166176.4 0 -14424.99897
215607.83 197452.9 0 -18154.94179
303758.19 304494.9 0 736.67082
320615.57 293494.9 0 -27120.66170
242393.03 198654.8 0 -43738.21311
329078.52 263208.0 0 -65870.47964
276826.67 263686.9 0 -13139.75644
220706.80 193284.5 0 -27422.32569
329093.58 330562.4 0 1468.83023
238841.71 221891.1 0 -16950.63906
190165.28 181958.5 0 -8206.81348
192530.75 178590.7 0 -13940.06939
235500.81 241349.9 0 5849.12133
220805.88 191670.3 0 -29135.59933
232037.87 198785.6 0 -33252.30551
223545.53 199388.0 0 -24157.55198
197688.02 174212.8 0 -23475.26210
230566.84 208896.1 0 -21670.77005
140800.63 142422.8 0 1622.17961
192363.31 187471.1 0 -4892.22076
135550.29 137738.7 0 2188.38476
128957.08 136684.5 0 7727.41280
203967.77 204098.0 0 130.21630
153598.26 155314.8 0 1716.57142
167395.69 164987.1 0 -2408.55742
111073.14 140885.7 0 29812.54736
169095.29 156433.1 0 -12662.17965
150230.56 166791.1 0 16560.58816
128097.21 157152.7 0 29055.51823
115875.20 142940.1 0 27064.95332
125827.90 155102.4 0 29274.47581
130139.33 160265.7 0 30126.36202
189829.18 190558.0 0 728.78195
233370.31 195824.7 0 -37545.65362
278239.38 254457.1 0 -23782.29535
280773.06 262474.4 0 -18298.67428
246943.68 189458.6 0 -57485.05191
198981.72 158280.7 0 -40701.03808
178810.16 158994.6 0 -19815.54577
175146.40 157052.9 0 -18093.48152
178809.63 161886.6 0 -16923.04738
165951.43 155527.7 0 -10423.69028
251362.53 197924.1 0 -53438.40491
179227.49 159330.5 0 -19896.95155
183229.79 180316.6 0 -2913.20730
188717.79 164618.8 0 -24099.01177
171989.30 153273.3 0 -18716.03328
271402.89 258600.8 0 -12802.04769
231573.66 221955.7 0 -9617.93814
189865.99 174793.1 0 -15072.87886
215871.02 197680.6 0 -18190.39255
176398.63 173782.3 0 -2616.29728
213298.26 196221.9 0 -17076.31944
191678.92 178455.7 0 -13223.25354
231858.34 198827.4 0 -33030.95480
202754.11 199517.8 0 -3236.27572
196636.21 192417.0 0 -4219.24268
198217.35 177500.3 0 -20717.00302
185709.97 174452.1 0 -11257.91576
166095.27 161699.7 0 -4395.59813
144655.86 162636.7 0 17980.83494
174646.01 172282.9 0 -2363.07834
104224.77 155298.7 0 51073.97575
145841.63 156863.4 0 11021.73176
167681.11 179519.4 0 11838.29165
166705.34 168293.6 0 1588.23352
147426.87 166320.9 0 18894.01575
161935.97 159942.0 0 -1994.01920
164513.93 190104.9 0 25590.91736
127752.79 156678.4 0 28925.64431
208867.65 196428.4 0 -12439.29427
165608.93 169802.2 0 4193.27329
118427.70 146116.0 0 27688.27417
87826.97 126216.3 0 38389.32893
120947.55 149031.9 0 28084.38515
173993.01 177758.8 0 3765.77739
137532.51 156615.8 0 19083.30888
171818.71 174718.8 0 2900.07559
180306.48 166018.1 0 -14288.42808
246707.66 226101.0 0 -20606.63075
205824.44 184762.3 0 -21062.12923
156713.98 149488.3 0 -7225.68850
215935.90 209480.2 0 -6455.69273
131479.77 157530.1 0 26050.35119
174322.38 174257.9 0 -64.44032
139485.15 171515.0 0 32029.81409
142993.99 154201.0 0 11206.98928
144192.00 157436.7 0 13244.68652
153905.73 163976.4 0 10070.70121
135460.63 156979.5 0 21518.82693
183930.66 183576.6 0 -354.09341
108850.51 145730.1 0 36879.59036
122736.34 155295.8 0 32559.49975
118893.26 146032.7 0 27139.48234
119100.56 148469.0 0 29368.39672
134265.32 158190.9 0 23925.58087
106950.44 143338.5 0 36388.01827
111375.05 136055.6 0 24680.55302
137035.11 155555.5 0 18520.36127
119778.09 151006.3 0 31228.25733
150685.16 155664.8 0 4979.60841
158577.05 154821.1 0 -3755.97541
154046.55 157515.4 0 3468.86155
255999.09 189157.5 0 -66841.56479
145892.24 163197.1 0 17304.85950
140576.06 163160.1 0 22584.04485
143811.86 142999.7 0 -812.14231
130516.51 144456.3 0 13939.76893
146773.13 159485.1 0 12711.97229
138139.01 158352.5 0 20213.47200
182865.55 184445.0 0 1579.46075
176753.83 170160.1 0 -6593.74649
131927.52 154705.5 0 22777.99595
87503.37 145896.8 0 58393.41983
102081.04 141805.4 0 39724.32124
118442.22 147152.6 0 28710.40639
145356.21 164434.7 0 19078.53356
99815.67 149549.0 0 49733.33856
78362.76 130837.3 0 52474.58855
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